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Field of interest

My general interests are in the area of the analytic number theory, with a special focus on Selberg's class and automorphic functions, transcendence problems, and exponential sums. I have also an interest in other branches of Number Theory and in applications of Number Theory to non-traditional fields, for example to the special functions.




Published Papers

42 S. Bettin, J. W. Bober, A. R. Booker, B. Conrey, M. Lee, G. Molteni, T. Oliver, D. J. Platt, R. S. Steiner, A conjectural extension of Hecke's converse theorem. to appear in Ramanujan J. (2017)
Pdf.
41 L. Grenié, G. Molteni, Explicit bounds for generators of the class group. to appear in Math. Comp. (2017).
Pdf.
40 L. Grenié, G. Molteni, Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH, II. to appear in Funct. Approx. Comment. Math. (2017).
Pdf.
39 L. Grenié, G. Molteni, A. Perelli, Primes and prime ideals in short intervals. Mathematika 6(2), 364-371 (2017).
Pdf. Abstract. DOI AMS Math. Review.
38 G. Molteni, Primes and prime ideals in short intervals. Boll. Unione Mat. Ital. 6(2), 364-371 (2016).
Pdf. Abstract. DOI AMS Math. Review.
37 A. Dudek, L. Grenié, G. Molteni, Primes in explicit short intervals on RH. Int. J. Number Theory, 12(5), 1391-1407 (2016).
Pdf. Abstract. DOI AMS Math. Review.
36 L. Grenié, G. Molteni, Inequalities for the Beta function. Math. Inequal. Appl., 18(4), 1427-1442 (2015).
Pdf. Abstract. AMS Math. Review.
35 L. Grenié, G. Molteni, Explicit smoothed prime ideals theorems under GRH. Math. Comp., 85(300), 1875-1899 (2016).
Pdf. Abstract. DOI AMS Math. Review. Data and PARI-GP commands available here.
34 L. Grenié, G. Molteni, Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH. Math. Comp., 85(298), 889-906 (2016).
Pdf. Abstract. DOI AMS Math. Review. Data and PARI-GP commands available here.
33 L. Grenié, G. Molteni, Zeros of Dedekind zeta functions under GRH. Math. Comp., 85(299), 1503-1522 (2016).
Pdf. Abstract. DOI AMS Math. Review.
32 A. Giorgilli, G. Molteni, Representation of a 2-power as sum of k 2-powers: a recursive formula. J. Number Theory 133(4), 1251-1261 (2013).
Pdf. Abstract. AMS Math. Review.
31 J. Kaczorowski, G. Molteni, Extremal values for the sum \textstyle \sum_{r=1}^\tau e(a 2^r/q). J. Number Theory 132(11), 2595-2603 (2012).
Pdf. Abstract. AMS Math. Review.
30 Y. Liu, Z. Lin, G. Molteni, D. Zhang, Eigenvalues and Equivalent Transformation of A Trigonometric Matrix Associated with Filter Design. Linear Algebra and Appl. 437(12), 2961--2972 (2012).
Pdf. Abstract. AMS Math. Review.
29 Z. Lin, Y. Liu, G. Molteni, D. Zhang, Spectral properties for a new composition of a matrix and a complex representation. Electron. J. Linear Algebra 23, 530-539 (2012).
Pdf. Abstract. AMS Math. Review.
28 G. Molteni, Representation of a 2-power as sum of k 2-powers: the asymptotic behavior. Int. J. Number Theory 8(8), 1923-1963 (2012).
Pdf. Abstract. AMS Math. Review.
27 G. Molteni, Cancellation in a short exponential sum. J. Number Theory. 130(9), 2011-2027 (2010).
Pdf. Abstract. AMS Math. Review.
26 G. Molteni, Multiplicity results for the functional equation of the Dirichlet L-functions. Acta Arith. 145(1), 43-70 (2010).
Pdf. Abstract. AMS Math. Review.
25 G. Molteni, Multiplicity results for the functional equation of the Dirichlet L-functions: case p=2. Acta Arith. 145(1), 71-81 (2010).
Pdf. Abstract. AMS Math. Review.
24 J. Kaczorowski, G. Molteni, A. Perelli, A converse theorem for Dirichlet L-functions. Comment. Math. Helv. 85(2), 463-483 (2010).
Pdf. Abstract. AMS Math. Review.
23 G. Molteni, Factorization in the extended Selberg class of L-functions associated to modular forms. Math. Nachr. 282(2), 232-242 (2009).
Pdf. Abstract. AMS Math. Review.
22 J. Kaczorowski, G. Molteni, A. Perelli, Unique factorization results for semigroups of L-functions. Math. Ann. 341(3), 517-527 (2008).
Pdf. Abstract. AMS Math. Review.
21 G. Molteni, An explicit bound for the error term of the development at s=1 of a set of lacunary series. Math. Inequal. Appl. 11(1), 173-188 (2008).
Pdf. Abstract. AMS Math. Review.
20 J. Kaczorowski, G. Molteni, A. Perelli, Some remarks on the unique factorization in certain semigroups of classical L-functions. Funct. Approx. Comment. Math. 37, 263-275 (2007).
Pdf. AMS Math. Review.
19 G. Molteni, The behavior of \sum_{n=1}^\infty \zeta^{\lfloor n\theta\rfloor}/n for special \theta. Acta Math. Hun. 117(1--2), 61-76 (2007).
Pdf. Abstract. AMS Math. Review.
18 G. Molteni, J. Steuding, (Almost) primitivity of Hecke L-functions. Monatsh. Math. 152, 63-71 (2007).
Pdf. Abstract. AMS Math. Review.
17 J. Kaczorowski, G. Molteni, A. Perelli, J. Steuding, J. Wolfart, Hecke's theory and the Selberg class, Funct. Approx. Comment. Math. 35, 183-193 (2006).
Pdf. Abstract. AMS Math. Review.
16 G. Molteni, E. Serra, M. Tarallo, S. Terracini, Asymptotic resonance, modes interaction and subharmonic bifurcation, Arch. Ration. Mech. Anal. 182 (1), 77-123 (2006).
Pdf. Abstract. AMS Math. Review.
15 J. Kaczorowski, G. Molteni, A. Perelli, Linear independence of L-functions, Forum. Math. 18, 1-7 (2006).
Pdf. Abstract. AMS Math. Review.
14 G. Molteni, About a question of Kannappan and Zhang, Result. Math. 47, 130-131 (2005).
Pdf. Abstract. AMS Math. Review.
13 G. Molteni, Limits of integrals involving almost periodic functions, Result. Math. 46, 361-366 (2004).
Pdf. Abstract. AMS Math. Review.
12 G. Molteni, General linear independence of a class of multiplicative functions, Arch. Math. 83, 27-40 (2004).
Pdf. Abstract. AMS Math. Review.
11 G. Molteni, Counting sets with exceptions, Math. Inequal. Appl. 7, 161-164 (2004).
Pdf. Abstract. AMS Math. Review.
10 G. Molteni, About two trigonometric matrices, Riv. Mat. Univ. Parma, 7, 261-273 (2004).
Abstract.
9 G. Molteni, About two trigonometric matrices, Linear Algebra Appl., 382, 39-59 (2004).
Pdf. Abstract. AMS Math. Review.
8 G. Molteni, Upper and lower bounds at s=1 for certain Dirichlet series with Euler product, Duke Math. Journal 111, 133-158 (2002).
Pdf. Abstract. AMS Math. Review.
7 G. Molteni, On the algebraic independence in the Selberg class, Arch. Math., 79, 432-438 (2002).
Pdf. Abstract. AMS Math. Review.
6 G. Molteni, Some arithmetical properties of the sequence \{\zeta(2k+1)\}_{k=1} and of its power series, Acta Math. Hun., 90 (3), 133-140 (2001).
Pdf. Abstract. AMS Math. Review.
5 G. Molteni, Existence of a non-entire twist for a class of L-functions, Acta Arith., XCIII.1, 53-65 (2000).
Pdf. Abstract. AMS Math. Review.
4 J. Kaczorowski, G. Molteni, A. Perelli, Linear independence in the Selberg class, C. R. Math. Rep. Acad. Sci. Canada, 21, 28-32 (1999).
Pdf. Abstract. AMS Math. Review.
3 G. Molteni, L-functions: Siegel-type theorems and structure theorems, February 1999. This is my Ph.D. thesis.
2 G. Molteni, A note on a result of Bochner ed Conrey-Ghosh about the Selberg class, Arch. Math., 72, 219-222 (1999).
Pdf. Abstract. AMS Math. Review.
1 F. Prati, L. Zucchetti, G. Molteni, Rotating patterns in Class-B lasers with cylindrical symmetry, Physical Review A, 51 (5), 4093-4108 (1995).
Pdf. Abstract.




Preprints

L. Grenié, G. Molteni, An effective Chebotarev density theorem under GRH. Arxiv.
A. Dudek, L. Grenié, G. Molteni, Explicit short intervals for primes in arithmetic progressions on GRH. Arxiv.
L. Grenié, G. Molteni, An improvement to an algorithm of Belabas, Diaz y Diaz and Friedman. Arxiv.




Lectures in N.T.

G. Molteni, Notes of the course Generators for the class group for the doctoral school 2016-2017 (Italian, handwritten).
G. Molteni, Notes of the course in Analytic Number Theory.
G. Molteni, Appunti per il corso di Teoria dei Numeri A.A.2003/04.
G. Molteni, Appunti per il corso di Teoria dei Numeri A.A.2002/03.
G. Molteni, Appunti per il corso di Teoria dei Numeri A.A.2001/02.